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In this paper we develop several algorithms for non-negative matrix factorization (NMF) in applications to blind (or semi blind) source separation (BSS), when sources are generally statistically dependent under conditions that additional constraints are imposed such as nonnegativity, sparsity, smoothness, lower complexity or better predictability. We(More)
In this paper we discus a wide class of loss (cost) functions for non-negative matrix factorization (NMF) and derive several novel algorithms with improved efficiency and robustness to noise and out-liers. We review several approaches which allow us to obtain generalized forms of multiplicative NMF algorithms and unify some existing algorithms. We give also(More)
In the paper we present new Alternating Least Squares (ALS) algorithms for Nonnegative Matrix Factorization (NMF) and their extensions to 3D Nonnegative Tensor Factorization (NTF) that are robust in the presence of noise and have many potential applications, including multi-way Blind Source Separation (BSS), multi-sensory or multi-dimensional data analysis,(More)
In this paper we derive a family of new extended SMART (Simultaneous Multiplicative Algebraic Reconstruction Technique) algorithms for Non-negative Matrix Factorization (NMF). The proposed algorithms are characterized by improved efficiency and convergence rate and can be applied for various distributions of data and additive noise. Information theory and(More)
Nonnegative Matrix Factorization (NMF) solves the following problem: find nonnegative matrices A ∈ R M ×R + and X ∈ R R×T + such that Y ∼ = AX, given only Y ∈ R M ×T and the assigned index R. This method has found a wide spectrum of applications in signal and image processing, such as blind source separation, spectra recovering, pattern recognition,(More)
The focal underdetermined system solver (FOCUSS) algorithm has already found many applications in signal processing and data analysis, whereas the regularized M-FOCUSS algorithm has been recently proposed by Cotter for finding sparse solutions to an underdetermined system of linear equations with multiple measurement vectors. In this paper, we propose three(More)
The most popular algorithms for Nonnegative Matrix Factorization (NMF) belong to a class of multiplicative Lee-Seung algorithms which have usually relative low complexity but are characterized by slow-convergence and the risk of getting stuck to in local minima. In this paper, we present and compare the performance of additive algorithms based on three(More)
Non-negative matrix factorization (NMF) is an emerging method with wide spectrum of potential applications in data analysis, feature extraction and blind source separation. Currently, most applications use relative simple multiplicative NMF learning algorithms which were proposed by Lee and Seung, and are based on minimization of the Kullback-Leibler(More)